After this question was first posed and considered I reported on some objections to my answer. If you haven’t already read those posts, I encourage you to do so now. Put briefly, both Marcus and Andre contend that particles must follow the immutable laws of physics. They argue (sensibly it would seem) that two identical worlds following identical laws must wind up in the same place. In this post I will defend that A) we cannot predict where those worlds will wind up, and in tomorrow’s B) even if we could, the results would be indeterminate.
My argument is that Universes starting from identical initial conditions will have different outcomes. I want to make very clear that his statement has nothing to do with our ability to predict those outcomes.
For instance, if we knew the position, velocity, temperature, etc. of every particle in the Universe at a given point in time, it might be reasonable to conclude that with perfect knowledge of the laws of physics, we could predict the outcome of the system. Of course, such computational ability would require resources greater than the Universe could provide. For example, if you built a computer that could run such a simulation, the simulation would have to take into consideration all parts of the Universe including the computer itself. It would have to have perfect knowledge about how the computer would evolve and how it would find the answer that it has yet to find”¦such a computer would also need at least as many atoms for computation as exist in the rest of Universe (to account for each particle), which is, of course, impossible.
The moral of the story is that regardless of whether or not the Universe evolves deterministically, no entity in that Universe could predict its outcome. That said, let’s agree to decouple the notions of predictability and outcome. For the sake of this discussion, I don’t care whether or not an outcome is predictable. My claim is that starting from identical initial conditions the outcomes themselves will not be the same. Tomorrow, I’ll explain why in greater detail.